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  <section id="module-sympy.physics.quantum.qapply">
<span id="qapply"></span><h1>Qapply<a class="headerlink" href="#module-sympy.physics.quantum.qapply" title="Permalink to this headline">¶</a></h1>
<p>Logic for applying operators to states.</p>
<p>Todo:
* Sometimes the final result needs to be expanded, we should do this by hand.</p>
<dl class="py function">
<dt class="sig sig-object py" id="sympy.physics.quantum.qapply.qapply">
<span class="sig-prename descclassname"><span class="pre">sympy.physics.quantum.qapply.</span></span><span class="sig-name descname"><span class="pre">qapply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">e</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">options</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/quantum/qapply.py#L26-L126"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.quantum.qapply.qapply" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply operators to states in a quantum expression.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>e</strong> : Expr</p>
<blockquote>
<div><p>The expression containing operators and states. This expression tree
will be walked to find operators acting on states symbolically.</p>
</div></blockquote>
<p><strong>options</strong> : dict</p>
<blockquote>
<div><p>A dict of key/value pairs that determine how the operator actions
are carried out.</p>
<p>The following options are valid:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">dagger</span></code>: try to apply Dagger operators to the left
(default: False).</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">ip_doit</span></code>: call <code class="docutils literal notranslate"><span class="pre">.doit()</span></code> in inner products when they are
encountered (default: True).</p></li>
</ul>
</div></blockquote>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>e</strong> : Expr</p>
<blockquote>
<div><p>The original expression, but with the operators applied to states.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.quantum</span> <span class="kn">import</span> <span class="n">qapply</span><span class="p">,</span> <span class="n">Ket</span><span class="p">,</span> <span class="n">Bra</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="n">Bra</span><span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">k</span> <span class="o">=</span> <span class="n">Ket</span><span class="p">(</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span> <span class="o">=</span> <span class="n">k</span> <span class="o">*</span> <span class="n">b</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span>
<span class="go">|k&gt;&lt;b|</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">qapply</span><span class="p">(</span><span class="n">A</span> <span class="o">*</span> <span class="n">b</span><span class="o">.</span><span class="n">dual</span> <span class="o">/</span> <span class="p">(</span><span class="n">b</span> <span class="o">*</span> <span class="n">b</span><span class="o">.</span><span class="n">dual</span><span class="p">))</span>
<span class="go">|k&gt;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">qapply</span><span class="p">(</span><span class="n">k</span><span class="o">.</span><span class="n">dual</span> <span class="o">*</span> <span class="n">A</span> <span class="o">/</span> <span class="p">(</span><span class="n">k</span><span class="o">.</span><span class="n">dual</span> <span class="o">*</span> <span class="n">k</span><span class="p">),</span> <span class="n">dagger</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="go">&lt;b|</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">qapply</span><span class="p">(</span><span class="n">k</span><span class="o">.</span><span class="n">dual</span> <span class="o">*</span> <span class="n">A</span> <span class="o">/</span> <span class="p">(</span><span class="n">k</span><span class="o">.</span><span class="n">dual</span> <span class="o">*</span> <span class="n">k</span><span class="p">))</span>
<span class="go">&lt;k|*|k&gt;&lt;b|/&lt;k|k&gt;</span>
</pre></div>
</div>
</dd></dl>

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